Enhancing TreeMMoSys with a high-precision strain gauge to measure the wind-induced response of trees down to the ground

Graphical abstract


Strain measurements
The developed sensor is based on the design presented for the first time in an earlier study [5], fully described in another study [6], and used elsewhere [7,22]. These studies show that strain (e) measured on tree parts, e.g., stem and branches, is linearly proportional to their displacement. This linear relationship can be exploited by means of a caliper type aluminum transducer tightly screwed to the tree parts at two points. The aluminum transducer carries four strain gauges (type Taidacent BF350, Taidacent, China) that measure its length variation induced by tree part motion. From these measurements, strain is calculated as: where DL is the wind-induced length variation of the aluminum transducer between the two mounting points with a distance (L) of 170 mm.
Since a temperature-dependent variation of the zero value of strain gauges was reported in earlier studies [5,7,22], we use a full Wheatstone bridge configuration with two active and two inactive strain gauges. In this configuration, the strain gauge is temperature-compensating by itself. Moreover, the full Wheatstone bridge configuration has a higher sensitivity than other Wheatstone bridge configurations [34]. We applied a TSS sampling frequency of 10 Hz for the measurement purpose presented here. The measured strain data is recorded with the TreeMMoSys ground receiver [33]. Fig. 1 compares TSS signals measured with half and full Wheatstone bridge configurations. The full-bridge configuration has higher sensitivity in measuring the applied loads [34,35]. The amplitude of the full-bridge signal is greater by about a factor of 2 ( Fig. 1a) than the half-bridge signal (Fig. 1b).

Power consumption and system output
The total power consumption adds from the TreeMMoSys ground receiver (0.13 A, [33]) and the number of TSS (26.3 mA per TSS) used. Using 10 TSS, the system can be operated by a 60 Ah 12 V battery for 152 h. The system can either be used calibrated or uncalibrated. In the uncalibrated case, the system provides information about the sway characteristics of the investigated tree part in the frequency or time-frequency domain. Calibrated sensors can also provide data on wood fiber length change from micro-to millimeters.

Data infrastructure
The voltage signals of the Wheatstone bridge are amplified by an HX711 signal amplifier. A WEMOS D1 mini microcontroller is used to read the HX711 output signals and sends them via Wifi to the TreeMMoSys ground receiver using the Message Queuing Telemetry Transport (MQTT) communication protocol (Fig. 2).

Design files
The design files for the ground receiver and the power supply were presented in an earlier study [33]. The schematic drawing of the aluminum transducer and the file to program the Wemos D1 mini is listed in Table 1.
The aluminum transducer and the extension arms can be milled into shape after Fig. 3. They have similar dimensions as the strain gauge transducer described earlier [6]. In the present work, the original design was modified to allow the full Wheatstone bridge circuit assembly. The cut-open-side of the aluminum transducer is 4.0 mm. This is wide enough to avoid contact of the open ends when the transducer is mounted to the sampled tree parts and under compression. If higher compressions are expected the size of the cut-open end can be modified accordingly.
The wiring of the strain gauges into a full Wheatstone bridge circuit and onto the HX711 as well as the connections to the Wemos D1 mini are presented in Fig. 4.

Bill of Materials
The Bill of Materials for the TreeMMoSys ground receiver and the power supply are described in a previous study [33]. For TSS it is given in Table 2.

Build instructions
The build instructions for the TreeMMoSys ground receiver and the power supply was presented in a previous study [33]. The build instructions for TSS are as follows: 1. See TreeMMoSys build instructions for ground receiver V2 [33]. 2. See TreeMMoSys build instructions for power supply V2 [33].    Fig. 3. The hole in the extension arm for the attachment to the tree parts has to be sized accordingly to the woodscrews intended to use. For usage on the stem, we found screws with 8.0 mm diameter sufficient; for usage on roots we used 4.0 mm diameter screws. 4. The following mounting of the strain gauges requires a work bench with a small vice. Briefly sand the selected mount surfaces for the strain gauges on the transducer. Clean the surfaces with isopropanol alcohol or a comparable detergent. Mark the exact position of the strain gauge with a pencil. 5. Take a strip of adhesive tape and lay it flat on the workbench, adhesive side looking upward. Use a tweezer to carefully take a strain gauge by a corner and stick it with the upward facing side onto the adhesive tape. Place the strain gauge with the tape on the intended position and stick it on one side onto the surface (Fig. 5a). Apply a small drop of instant adhesive on the intended position of the strain gauge on the aluminum transducer. Roll the adhesive tape with the strain gauge sticking under it evenly onto the drop and the strain gauge on it in the intended position. Apply thumb pressure for roughly a minute by placing your thumb onto the tape. The warmth will help to cure the instant adhesive. Remove the adhesive tape by pulling carefully at a shallow angle (Fig. 5b). 6. Apply a thin coat of liquid rubber directly onto the strain gauge to protect it from moisture. It is recommended as the glue deteriorates with exposure to humidity over time.  7. Solder the full Wheatstone bridge: Cut a hole grip board to a size of 3 Â 12 holes to make the solder point. Apply a sufficient amount of solder to it and solder the wires of the strain gauge according to Fig. 4. Solder the connections between the soldering point and the corresponding pins of the HX711 board with the enameled wire, as well as the connections between the HX711 and the Wemos D1 mini. 8. Mount the soldering point, the HX711, and Wemos D1 mini with a short piece of double-sided-adhesive-foam-tape onto the aluminum transducer, covering all electric connections on the bottom site of these items. This is used to ensure an electric isolation and avoid electric shortcuts. 9. Cut the twin-stranded wire into 15 cm pieces and solder the male micro USB ports onto one end of the wires. Via these wires the system will be powered in the field, by connecting the male micro USB ports with the female micro USB ports on the WEMOS D1 mini. The cut-open end will be connected with the power supply. 10. Install the Arduino desktop application onto your PC [38]. Add the URL https://arduino.esp8266.com/stable/package_ esp8266com_index.json to the ''additional board managers" option, found in the app settings. Connect one WEMOS D1 mini via a micro USB cable to your PC. Load the TSS.ino script (available online: https://osf.io/p8h6k/) onto the WEMOS D1 mini, make sure to set ''Sensor_ID" to a continues number and adapt -if necessary -the SSID, following the instructions for the sensor setup described in an earlier study [33]. Check the function of the sensor by looking at the serial monitor. The successful mounting of the strain gauges can be tested by applying small loads on the extension arms. 11. Trouble shooting: a. If the message ''HX711 can't be found" appears, check the connection and power connection between the HX711 and WEMOS D1 mini. b. If the sensor reading is a fixed value, the HX711 works fine, but the solder point is connected incorrectly. 12. If everything works, cover all electronics with a thin layer of conformal coating to enable the TSS deployment in the field. 13. Prior to the installation, wrap TSS in a 1 m Â 1 m piece of a space blanket to provide radiation shielding.

TSS calibration
For calibration, the extension arms of the TSS are attached to two adjustable wood blocks connected with a fine threaded rod. In the rest position, the width of the cut-open-side is 60.0 mm. We applied loads using the threaded rod until its width increased to a maximum of 61.5 mm. In 0.3 mm steps TSS was returned to its rest position and further compressed to 58.5 mm. All positions are kept for 30 s. The resulting calibration curve converts the voltage (mV) output of the Wheatstone bridge to DL (mm). The length change DL can be used to calculate e according to equation (1). TSS responds to forces as low as 0.0098 N, which minimizes local tree part rigidification and makes it useable at all tree parts sampled in this study. To measure the above-ground response of the sample tree to wind loading, four TSS were mounted perpendicularly to an 18.6 m high Scots pine (Pinus sylvestris L.) tree at height z 2 = 1/7H and the stem base (z 1 = 0.2 m) to measure the stem strain in east-west (e x ) and north-south (e y ) directions (Fig. 6). The height z 2 = 1/7H height is assumed to represent the first antinodal point of vibration of a clamped-free beam and can be used to determine the wind-induced sway pattern [19,40]. Additionally, one Tree Response Sensor (TRS) [33] each was installed at z 1 and z 2 to measure stem tilt (T) in east-west (t x ) and north-south (t y ) directions. The TRS measurements were used to compare the temporal dynamics of stem tilt and marginal wood fiber strain. Four TSS were mounted on the upper site of three exposed main roots 0.15-0.50 m away from the stem base to monitor the root response to wind loading.

Field measurements
The strain gauge extension arms were tightly screwed to the sampled tree parts at two points to prevent inaccurate measurements. To minimize strain gauge heating, we wrapped the sensors in space blankets.
The components of the 3D wind vector above the forest canopy were measured with an ultrasonic anemometer (type 81000VRE, R.M. Young Company, USA) installed on a 23 m scaffold tower. The horizontal distance between the ultrasonic measurement and sample tree was 6 m. The measured wind vector components were used to calculate the momentum flux (M), which is used to approximate the wind load acting on the sample tree [12].

Tree pulling tests
Non-destructive static (SPT) and pull-and-release (PRPT) pulling tests validated TSS in the field under calm conditions. Two commercially available TreeQinetic (PTQ) elastometers (Argus electronic, Germany) were mounted next to the two TSS at the same height and directions as reference devices. They are typically used to measure strain of the stem during pulling tests, a standardized procedure to monitor the tree resistance against external loads [41]. The sample tree was subjected to two SPT and PRPT to validate TSS measurements. A 3-fold pulley (CT -Climbing Technology, Italia) combined with the PiCUS TreeQinetic system was used for the pulling tests. A pulling rope (Dyneema, Dynamica Ropes ApS, Denmark) was attached to the stem at 60 % of the tree height. The pulling force was increased until a stem base inclination of 0.25°was reached to prevent primary tree failure [42].

Data processing
Outliers in the 10 Hz TSS data were removed using a Hampel filter. To remove drifts in the data, frequencies outside 0.003 to 2.5 Hz were attenuated using a bandpass filter. The same procedure was applied to the TreeQinetic elastometer data.
From the time series of directional strain measurements at the stem, e x and e y , the strain vector magnitude E was calculated: On three primary roots (RT1-RT3), the strain was measured one-dimensionally along the longitudinal root axis (e RT1 , e RT2 , e RT3 ). These measurements were carried out to study root response on the external loads acting on the above-ground tree parts. Two TSS were attached to northeast-facing RT1 (azimuth: 50°) at 15 cm (root diameter: 17.0 cm) and 50 cm (root diameter: 8.5 cm) distance from the stem base. One TSS was mounted to southwest-facing RT2 (root diameter: 5.3 cm; azimuth: 210°) and west-facing RT3 (root diameter: 5.5 cm; azimuth: 270°) at distances 43 and 38 cm from the base of the stem.   The time series of stem tilt components t x and t y were used to compute the tilt vector magnitude T [33]: The fluctuations of the wind vector components u (u 0 ), v (v 0 ), and w (w 0 ) were the basis for the above-canopy momentum flux (M) calculation [43]: To analyze and compare the frequency response of TRS and TSS, Welch power spectral density (PSD) estimates were calculated from the 10 Hz time series of E and T. The PSD calculation was performed over half-hourly intervals (18000 data points each). All spectra were normalized with their maximum to ensure their comparability.

Spectral analysis
The mean normalized E and T Welch spectra are similar (Fig. 7), showing three local PSD maxima. The first maxima are caused by coherent turbulent structures in the above-canopy airflow passing the measurement site with 0.04 to 0.05 Hz fre- quencies. The second maximum is located in the range of the fundamental sway frequency (f 0 = 0.26). The third maximum indicates a harmonic (f 1 = 0.51) induced by the multimodal tree response to wind loading.

Tree pulling test results
The measurement results of TSS and PTQ during the pulling tests are very similar, and the coefficient of determination (R 2 ) between the analyzed data is at least 0.993. During all pulling tests, the E values measured with TSS and PTQ rise steeply with increasing force.
During the first static pulling test (Fig. 8a), they reach maximum values of 929 and 935 lE. Slightly higher E values at 965 and 976 lE were measured during the second static pulling test (Fig. 8b). After the maximum strain was recorded, the pull- ing force was gradually reduced until the sample tree returned to the rest position. The difference between the maxima of the TSS and PTQ measurements is less than 1 %. The mean absolute errors (MAE) associated with the TSS and PTQ measurements during the static pulling tests are MAE = 6 lE and MAE = 5 lE.
Similar good results were obtained for the two pull-and-release tests. The TSS and PTQ devices achieved a similar performance in the two tests shown in Fig. 8c and 8d. Like the static pulling tests, E measured with TSS and PTQ rises rapidly with increasing pulling force. After the E maximum was reached, the tree was released from the pulling rope to allow it to swing freely to its rest position. The decay of E is visible as an oscillating part of the represented time series. For the first pull-andrelease test, MAE = -2 lE; for the second test MAE = 4 lE.

Monitoring wind-induced tree response
Time series of 100 s mean (block average of 1000 samples) values of wind-induced E calculated at z 2 = 1/7H from TSS measurements are shown as an example for 29-30 June 2021 in Fig. 9a. The E mean values are presented with 100 s mean M values approximating the above-canopy wind load pattern. They are strongly correlated (R 2 = 0.88), and their correlation is slightly higher than the correlation of T measured with TRS and M (R 2 = 0.84) displayed in Fig. 9b. Based on this exemplary comparison of TSS and TRS, it can be concluded that TSS achieves at least similarly good measuring results as TRS, which has already been used in earlier studies [12,33]. The linear relationship between T and E is displayed in Fig. 9c (sampling rate 10 Hz). It shows a tight correlation between E and T, with R 2 = 0.83. Fig. 10 presents 300 s sequences of measured root and stem strain (sampling rate 10 Hz). The time series shown for the two points along northeast-facing RT1 (growing in the main wind direction) are similar (R 2 = 0.87), with larger e RT1 measured closer to the stem base (Fig. 10a). The amplitudes of e RT2 measured at southwest-facing RT2 (growing against the main wind direction) match (R 2 = 0.97) the amplitudes of e RT1 but in the opposite direction. RT1 and RT2 growing at the opposite sides of the stem base show an antagonistic response pattern (Fig. 10b).
The response of RT3, oriented to the west, is less pronounced and weaker coupled with the response of RT1 (R 2 = 0.56) and RT2 (R 2 = 0.39). The response of RT1 and RT2 follows the strain pattern measured at the stem base (Fig. 10c). Their reactions are more strongly correlated with E (R 2 = 0.75 and R 2 = 0.76) than the reactions of RT3 (R 2 = 0.42). The correlation between the response of the stem and the monitored roots indicates the dynamic transfer of elastic energy induced by wind loads acting on the aboveground tree parts to the roots.

Conclusions
The instructions summarized in this article allow the inexpensive Tree Strain Sensor TSS assembly. It reproduces the measuring results of a commercially available standard in the field. The use of the full-bridge configuration yields better results than the previously used half-bridge configurations. It is possible to precisely measure the response of tree parts to external loads such as pulling tests and natural wind loading. The straightforward integration of TSS into TreeMMoSys allows easy, wireless, and synchronized data collection from multiple TRS and TSS with one system and increases the range of TreeM-MoSys applications. The integrated system makes it possible to track the vibration behavior of tree parts down to the ground. Its widespread use helps gather crucial information to understand better wind-tree interaction and the formation of storm damage in forests.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.